A combinatorial property of languages and monoids

摘要

In a 1976 paper, B.H. Neumann characterized center-by-finite groups as being groups with a particular combinatorial property; a group is center-by-finite if and only if every infinite sequence of its elements contains a pair of elements that commute. The characterization was produced as an answer to a question by Paul Erdoes and has led to a series of papers by various authors in which combinatorial properties of algebraic structures have been investigated. A survey of this direction of research, by the first author, appears in. Our aim here is to investigate formal languages that satisfy particular combinatorial properties (namely, permutational properties) with respect to combinatorial and finiteness properties of their syntactic monoids.